Approximating Maximum Edge 2-Coloring in Simple Graphs

Chen, Zhizhong; Konno, Sayuri; Matsushita, Yuki

doi:10.1007/978-3-642-14355-7_9

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Tuza's Conjecture1

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Cited by 2 publications

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“…The problem of finding lower bounds on α ′ k (G) has been studied by several authors [3,8,16,21,24], usually with the goal of finding approximation algorithms. While Theorem 4.6 gives a lower bound on α ′ k (G), the same bound applies even for "small" maximal k-edge-colorable subgraphs of G, and therefore typically will not be sharp.…”

Section: Tuza's Conjecturementioning

confidence: 99%

Maximal k-edge-colorable subgraphs, Vizing’s Theorem, and Tuza’s Conjecture

Puleo

2017

Discrete Mathematics

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Abstract. We prove that if M is a maximal k-edge-colorable subgraph of a multigraph G and if(When G is a simple graph, the set F is just the set of vertices having degree less than k in M .) This implies Vizing's Theorem as well as a special case of Tuza's Conjecture on packing and covering of triangles. A more detailed version of our result also implies Vizing's Adjacency Lemma for simple graphs.

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